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Prove that FG passes through the midpoint of AC (18)

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October 29, 2010

geometryparallelogramincentergeometric transformationhomothetyprojective geometrygeometry unsolved

Problem Statement

A point

B

lies on a chord

AC

of circle

\omega.

Segments

AB

and

BC

are diameters of circles

\omega

and

\omega_2

centered at

O_1

and

O_2

respectively. These circles intersect

\omega

for the second time in points

D

and

E

respectively. The rays

O_1D

and

O_2E

meet in a point

F,

and the rays

AD

and

CE

do in a point

G.

Prove that the line

FG

passes through the midpoint of the segment

AC.

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